Michelle and Barack are hosting a delegation of foreign dignitaries. She brings
ID: 1515813 • Letter: M
Question
Michelle and Barack are hosting a delegation of foreign dignitaries. She brings 2 liters of chilled white wine at a temperature of 2 degree C, while he brings 4 liters of the same type of wine straight from the store at 20 degree C. They decide to make the best of it and mix the two together.(The container the process.) The specific heat of wine is C = 4 kJ/kg*K, and its density is 1 kg/liter. When mixed, what is the final temperature of the mixture in degree C? What is the amount of heat transferred from Barack's wine the Michelle's? How much heat needs to be extracted from the mixture in order to cool it down to 0 degree C? In order to effect this final chilling, the White House Chief of Staff brings some of it to the wine mixture. The latent heat of fusion of ice is 336 kJ/kg. How much ice should be added so that the wine is cooled all the way to 0 degree C but does not leave any tell-tale ice chips floating in the container?Explanation / Answer
C = 4KJ/KG k
Density = Mass/Volume
Mass = 1 Kg/lt * 2 lt
Mass = 2 Kg
m1 = 2 Kg @ 2
m2 = 4 Kg @ 20
(A)
Let the final Temperature be Tf.
m1*C*(Tf - 2) = m2 * C*(20 - Tf)
2 * (Tf - 2) = 4 * (20 - Tf)
Tf = 14 oC
Final Temperature , Tf = 14 oC
(B)
Heat Transferred from Barack's wine, Q = m1*C*(Tf - 2)
Q = 2 * 4 * 12 KJ
Q = 96 KJ
(C)
In order to bring the mixture down to 0 oC
Heat to be Extracted,
Q = m * C * T
Q = 6 * 4 * (14 - 0) KJ
Q = 336 KJ
(D)
Let the mass of ice be m.
m*336 KJ = 336 KJ
m = 1 Kg
Mass of ice needed = 1 Kg